Related papers: A Hamiltonian approach to implicit systems, genera…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$…
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…